It appears that circles are not being properly cut by the Break Out Segment command with the Remove Segment disabled.

Test case:

Step 1: Create a circle.Step 2: Draw a triangle with one vertex at the center of the circle and the other vertices outside the circle.Step 3: Execute "Break Out Segment" with "Remove Segment" unchecked.Step 4: Select the arc defined by the two legs of the triangle with an end point at the center of the circle.

On my system this results in the removal of the arc, whether or not the "Remove Segment" option is checked.